Hi Mark and Diana,
There is an English speaking playgroup called Hedgehogs. It is on Södermalm and held every Friday afternoon from 2pm - 5pm. It costs 30kr. I am sure they do not do any formal teaching of English but it may be worthwhile attending to see if any of the other parents are aware of the type of group you are looking for. It will be great for you little ones to meet friends anyway.
www.hogalidhedgehogs.com/ I am not sure if it runs over the summer though????
Also there is another website called
www.mumsinsweden.com/ This if for English speaking parents of any nationality. I used this site when I fell pregnant to help me navigate the all sorts of things in Sweden that I had no clue about when it came to children. I am sure a post on there will help you no end in both finding playmates for the kids and also English classes, formal or informal.
Hope this helps
Hels